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Use of the phrase "at least"

Hello,

I am slightly confused on the use of the phrase "at least" when used in different contexts with regards to time...

My first example would be the following:
"I will be gone until at least 8:00", this sentence suggests to me that the person will be back at 8:00 at the earliest but it could also be any time past 8:00.

My second example would be:
"I will be home by at least 8:00", this sentence suggests to me that the person will be home anytime before 8:00 or 8:00 at the latest.

I have heard this phrase used both ways by people, are they both correct to use and if so have I interpreted them properly?